Background

The research project aims to investigate the boundary layer on the vibrating surface thorough experimental and numerical methods. As investigated in the work from Bergan (2019) and Tengs (2019), the fluid-hydrofoil coupled system can be assumed as a one degree of freedom system (SDOF system). This means that the system is governed by Newton’s second law of motion and is therefore f(mass, damping, stiffness, force). Among these parameters the damping factor has not been much addressed in the literature despite being critical when runner vibration is around resonance frequency (Monette et al., 2014). The theory behind this phenomena has been studied in the paper from Monette et al. (2014). Hydrodynamic damping investigation in singular hydrofoil configuration with different shapes has been carried out by both Bergan (2019) and Coutu et al. (2012). Bergan (2019) have also investigated a linear blade cascade of 3 double-fixed hydrofoils in a cavitation free test rig. The single hydrofoil research has found a linear relationship between damping ratio and water velocity, and a different gradient of this relationship depending if water velocity is below or above the lock in region. When water velocity is below lock-in the linear relationship gradient is slightly positive and almost constant, while above lock in the gradient is largely positive. Moreover the almost linear relationship in the area of velocity below the lock-in is maintained also for the structural natural frequency while is somehow disrupted above lock-in region where no further trends could be founded. Regarding the linear blade cascade work Bergan (2019) has stated that three blade system behaves as a one bladed system while doubts have been raised on the behaviour of a circular cascade configuration. The interaction between fluid and the structure takes place at the interface/boundary layer, moreover a strong interaction between blades and the surrounding water, which led to change of damping characteristics (Trivedi & Cervantes, 2017) has been demonstrated. Further investigations were performed using different trailing edge profiles and their interaction with the vortex shedding (Sagmo, 2021). Flow characteristics were studied in detail including the turbulent properties for different Reynolds numbers. The research clearly indicated a radial arrangement of the hydrofoil is essential to mimic the the turbine blade effect (Pirocca, 2020). The radial cascade, aim of this PhD, will help to understand how blades react to forced excitation and the interaction between neighbouring blades, with a focus on the hydrodynamic damping effect for a circular configuration.

The phase 1 experiments will be carried out on a circular blade cascade which improved version of previous work in the Waterpower laboratory. The original work (2016 - 2019), as stated above, focused on a single hydrofoil test case and the hydrodynamic damping with respect to the flow Reynolds number was studied. Later, the work extended to three hydrofoils arranged parallelly to study the impact of nearby structure on the hydrodynamic damping. Moderate impact on the added mass was seen during this study. However, in the linear arrangement, the acoustic waves are normal to the blade surface. When it comes to hydraulic turbine, the blades are arranged in circular pattern, which is different from the linear arrangement of the hydrofoil. This work further extended to circular arrangement of the hydrofoils to study impact of circular pattern during resonance condition.

Background

Our prior studies in the Waterpower laboratory clearly indicated that the nearby wall has significant impact on the added mass of the neighbouring structure. As we know, hydraulic turbines include several components and each play a critical role in altering the added mass and the eigen frequencies. Moreover, the turbine runner is rotating, and  that adds new dimension to the complexity of the present fluid structure interaction. Available knowledge is limited, specifically vibration induced fatigue. We need robust mechanism to predict the blade resonance. The research gap is addressed in the article (C. Trivedi, Engineering Failure Analysis, 77 (2017) pp. 1–22). To address these challenges, we have developed a simplified test rig of rotating disc that allows us to conduct study on various influencing parameters. The test rig allows us changing distance of nearby wall, angular speed, submergence level. 

The important objective is to understand the physics focusing on how surrounded bulk flow reacts to the resonating plate, and how wall proximity causes the change of natural frequency (added mass). This will help us to develop mathematical relation in the context of natural frequency and the nearby structure. The mathematical relation will be developed further for more complex situation, then turbine blade.

Objectives

1. Investigate the change of natural frequency of a plate with respect to the proximity of the rigid wall.
2. Investigate the flow physics around the resonating plate, focus on possible source and sink pattern.
3. Interpret the flow pattern, wall proximity and the change of natural frequency (added mass).
4. Develop correlation of point 3 and check Kwak’s theory holds true  (or method presented by Askari et al.) and can be extended to the turbine blades.

Background

Damping is divided in three categories: (1) fluid added (hydrodynamic) damping, (2) structural (friction) damping and (3) material damping. Hydrodynamic damping is dependent on change in mode-shape due to fluid pressure, convection through vortex shedding, viscous effect within the boundary layer, flow velocity, surface roughness, proximity of nearby structure and submergence level. We have seen that when a structure subject to a specific mode-shape, it deforms. The deformation affects the flow field, particularly close to the antinode boundary of the vibrating structure. This results in rapid change of pressure and velocity. It is important to understand that what happens in the boundary layer when a structure vibrates at resonant frequency and undergoes different mode-shapes, e.g., how viscosity, inertia and shear stress change within the boundary layer. During resonance, amplitudes close to the vibrating wall follows sinusoidal pattern; small amplitudes at the node-point and high amplitudes at the antinode-point. Thus, pressure gradient constantly changes from favorable to adverse; similarly, Reynolds stresses and viscous effect. In the boundary layer, a three-dimensional fluid element will travel upstream and downstream as flow accelerate and decelerate depending on mode-shape. The reverse flow occurs in regions of low kinetic energy (near to vibrating node point) and the large eddies, which bring outer-region momentum towards the wall, supply some downstream flow. Generally, three regions are created when backflow occurs.

the goal of this work will be closing the knowledge gap on behavior of hydro dynamic damping focusing mainly on the change in boundary layer during resonance and its effect in damping.  Boundary layer flow instability caused by mainly kinetic energy functions resulting from high-frequency vibration of the blade structure will be studied to understand the relation between the boundary layer and the damping effect. In order to achieve this, first coupled FSI using ANSYS will be carried out so that the flow physic around vibrating body can be understood. Then, a small test rig with simple geometry is planned to build in the laboratory in which PIV measurement will be implemented for flow characteristics, excitation will be provided by piezoelectric patches and response will be registered with the help of strain gauge. In the later part, the experiments will be scaled to hydrofoil type structure to study the impact of pressure gradient. Stepped sine types of frequency excitation will be used such a way that transient can be avoided. For numerical investigation, high-quality numerical simulations like LES and DNS will be used. First, the simulation will be carried out using a relatively simple model and gradually complexity will be increased to reach the desired results.

The boundary layer has essential role to create damping effect. We have developed a dedicated benchmark test rig in the Waterpower laboratory to study flow phenomena in an isolated environment. The test rig is highly versatile allowing us to carry out numerous experiments of different types addressing the fundamentals of fluid dynamics and fluid structure interactions. We plan to use this test rig with rectangular cross section, and aim to integrate a reverberating longitudinal plate into the test section and investigate the boundary layer at different Reynolds numbers.